Design andAnalysis ofaTwoStage Traffic Light System Using Fuzzy Logic

Figure 1:
General Structure of intersection.
Phase-1 
Phase-2 
Phase-3 
Phase-4 
Figure 2:
Phases of Traffic light.
Symbol
Lane
Movement Allowed
EL 1
East Lane- 1
Straight and left
EL 2
East Lane- 2
Right
WL 1
West Lane- 1
Straight and left
WL 2
West Lane- 2
Right
NL 1
North Lane- 1
Straight and left
NL 2
North Lane- 2
Right
SL 1
South Lane- 1
Straight and left
SL 2
South Lane- 2
Right
Table 1:
Notation.

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Volume 5 • Issue 3 • 1000162
J Inform Tech Softw Eng
ISSN: 2165-7866 JITSE, an open access journal
Citation:
Alam J, Pandey MK (2015) 
Design and Analysis of a Two Stage Traffic Light System Using Fuzzy Logic. 
J Inform Tech Softw Eng 5: 162. 
doi:
10.4172/2165-7866.1000162
Page 5 of 9
Phase1= maximum (WL1, EL1)
Phase2 = maximum (WL2, EL2)
Phase3 = maximum (NL1, SL1)
Phase4 = maximum (NL2, SL2)
Vehicle arrival distribution
There are four phases or approaches in this isolated intersection 
model with twelve total movements and a server traffic light. Each phase 
consists of three movements which are through movement, right and 
left turn movements. This model is based on an M/M/1 queuing theory 
using three basic concepts of queuing theory i.e., customer, queue, 
and server. The first and the second M in M/M/1 stand for memory 
less distribution of inter-arrival times and service times respectively. 
The “1” indicates that the isolated intersection has single server, which 
means one traffic signal, to service single signal phase at one time [19].
In this model First-In-First-Out (FIFO) principle is applied to the 
vehicles queue. The vehicles are known as customers while services 
time is the time for the vehicles to depart and to cross the intersection. 
Traffic at the intersection arrival and service time are independent 
random variables with Poisson distribution.Therefore, the arrival of 
vehicles at the intersection with arrival rate λ and the average of the 
inter-arrival times between vehicles are 1/ λ. The arrival of the vehicles 
in a Poisson process and the time period in order to reach the number 
of vehicles is as follows Poisson distribution.
( ) .
( )
x 0, 1, 2, 3,........
!
X
t
t e
P x
x
λ
λ
−
=
=
Where P(x) is the probability of vehicles x during counting interval 
t and λ is the average arrival rate per unit time, t is the duration of each 
counting interval.The vehicle arrival rate is 0~1 per second.
Put n= λt, where n is the average number of vehicles during 
counting interval. The equation can be written as follows
!
.
)
(
x
e
n
x
P
n
X
−
=